Solve for $x$ and $y$ using substitution. ${-3x-4y = -2}$ ${y = 2x-5}$
Solution: Since $y$ has already been solved for, substitute $2x-5$ for $y$ in the first equation. ${-3x - 4}{(2x-5)}{= -2}$ Simplify and solve for $x$ $-3x-8x + 20 = -2$ $-11x+20 = -2$ $-11x+20{-20} = -2{-20}$ $-11x = -22$ $\dfrac{-11x}{{-11}} = \dfrac{-22}{{-11}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 2x-5}\thinspace$ to find $y$ ${y = 2}{(2)}{ - 5}$ $y = 4 - 5$ $y = -1$ You can also plug ${x = 2}$ into $\thinspace {-3x-4y = -2}\thinspace$ and get the same answer for $y$ : ${-3}{(2)}{ - 4y = -2}$ ${y = -1}$